I am conducting a combination of continuous and categorical variables and am trying to find how to get additional fit indices other than chi-square and RMSEA with the original version of Mplus. Is this possible? If so, how?

Version 1 did not provide fit statistics other than chi-square and RMSEA. Version 2 does. You would have to compute them yourself if you want other fit measures and are using Version 1. There are several postings on Mplus Discussion that give formulas for alternative tests of fit.

A student with whom I am working is doing a path analysis with all of the variables in her model being binary. She has estimated logistic regression coefficients with SPSS-PC, which does not provide standardized coefficients. Is it possible to calculate indirect and total effects with the unstandarized coefficients, given the variables' metrics are all 1/0? If not, could you direct me to a reference that would show how standardized coefficients could be calculated? Thank you.

The analogy with regular continuous dependent variable calculations of direct and indirect effects can be used when applying Mplus. Mplus considers latent continuous response variables y* (one behind each categorical dependent variable). The unstandardized estimates would be used here.

Hello: I am Ph.D. candidate at Washington State University, Pullman. Currently I am working a paper where I am using MIMIC model (Multiple Indicators and Multiple Causes (Goldbergers' MIMIC Model). Can I estimate this MIMIC model using Mplus? I am new to Mplus, and therefore I am unable to use it. Please advice me how?

PS: My MIMIC model is as follows: Suppose I have a single latent variable which we call health status (h). Latent health status has many observable indicators say, (Y, which is a vector). Moreover, the latent health status has many cause variables say (X-vector). So we have a problem where the latent variable (h) is a linearly determined by vectors of cause variables (X), and the latent variable (h) in turn determines the vector of indicators variables (Y).

(1) h= alpha*x+ error term (2) y= beta*h+ error term

Then the reduced model is: y=alpha*beta*x+ error term

Now, I want to estimate the latent variable h, coefficients alpha and beta.

Chapter 18 of the Mplus User's Guide has examples showing how to set up a MIMIC model. You can also find examples at www.statmodel.com under Examples, Continuous Outcomes, Factor analysis with covariates. A MIMIC model is a confirmatory factor analysis model with covariates.

I think you refer to an indirect effect, that is a product of two slopes. If that is correct, Mplus Version 3 gives the standard error for this indirect effect. Testing difference (or rather equality) across groups would seem straightforward if there are no across-group parameter equality constraints because then the difference test is based on uncorrelated parameter estimates. So you only use the SEs for each indirect effect. If there across-group constraints, you would need to use covariances between parameters in the different groups which isn't readily available for indirect effects, but would have to be worked out via the Delta method.

I've heard about the possibilty to compute 'indiect effects' now. If this is correct, can you tell me what is to do in the Syntax to examine this effect? May be you have some 'zipped' examples here in a chapter on the homepage?

Mplus does censored-normal modeling (= Tobit), and also allows for "inflation" at the censoring point (so a 2-class model in line with ZIP). I am not sure what you mean by marginal effects - the model-estimated means and variances are produced.

Hi, I have two ordinal (ordered categorical) endogenous variables Y1 and Y2:

ANALYSIS: PARAMETERIZATION=THETA; TYPE=MEANSTRUCTURE;

Y1 ON Y2 X1 X2 Y2 ON X2 X3

MODEL INDIRECT: Y1 IND Y2 X2

The indirect effect is significant. I know how MPLUS gets the coefficient of the indirect effect, but I don't know how it gets the standard error. Could you please answer this question for me? Thanks a lot!

Hello. I am running a path model in MPlus v. 3.12 and am examining indirect effects. I am confused by some of the results. I am finding many significant indirect effects (as gauged by the Est./S.E. values), but all of these effects have extremely low coefficients. For example, many of the significant indirect effects have STD and StdYX values of .0002 or .0004. I do not understand how such small coefficients can be significant. Am I missing something?

A quick follow-on to my question above. First, I made a mistake above - the effects are reported to three not four decimal places. So, I meant to say that there are several effects around .002 or .004.

Second, I am noticing that there are several situations where the indirect effect is larger (and significant) than the total effect (which may be nonsignificant). I thought the total effect included the indirect effect, so I don't understand how this can be. Can you clarify this for me.

Hi, thanks a lot for your reply to my previous inquiry on June 14. Back to my model with two ordinal (ordered categorical) endogenous variables Y1 and Y2:

ANALYSIS: PARAMETERIZATION=THETA; TYPE=MEANSTRUCTURE;

Y1 ON Y2 X1 X2 Y2 ON X2 X3

MODEL INDIRECT: Y1 IND Y2 X2

In the output, Mplus gives Estimates, S.E., and Est./S.E. for both direct and indirect effects. Is Est./S.E. the z-score, from which we can calculate probabilities? For both direct and indirect effects? And, for both DELTA and THETA PARAMETERIZATION?

I want to confirm this because Mplus doesn't report probibilities for one- or two- tailed tests. Thanks again!

When standardized coefficients for indirect effects are calculated, which variables provide the standard deviations for standardization? For example, if A -> B -> C, the indirect effect of A on C is beta(AB)* beta(BC). Are the standardized coefficients (StdXY) to be interpreted as the change in C, expressed in terms of a fraction of one standard deviaiton, that occurs as a result of one standard deviation change in A? Or is B involved somehow also?

Sorry to bother you again. Just a quick question. Have you incorporated total effect calculations into Mplus with SE's. yet? The new manual seems to indicate it but I can only see total indirects. Thanks.

We have always given the total effect with a standard error. It depends on how you specify MODEL INDIRECT. In some specifications, it is referred to as sum of indirect effects. If you want more information, please send your input, data, output, and license number to support@statmodel.com.

Sorry, I must not have made myself clear. Take for example this simple model:

TITLE: this is an example of a path analysis with total effects DATA: FILE IS my.cov; type is covariance; nobservations are 100; VARIABLE: NAMES ARE y1 y2 x1; MODEL: y1 on y2 x1; y2 on x1; MODEL INDIRECT: y1 ind y2 x1;

--------------------- The total effect of X1 on Y1 would be the direct effect of X1 on Y1 = 0.060 plus the indirect effect of X1 on Y1 = 0.190, with the total effect of X1 on Y1 as 0.250 (se= 0.117). How would I get these total effects and standard errors?

I'm running a path model with a set of endogenous variables both continous and binary. In such cases, how are the total and indirect effect estimates scaled? The outcome is dichotomous so I believe they are logits, but wanted to double check.

Typically, I have found that when there is a statistically significant total effect the direct, indirect, or both are also statsitically significant.

However, I have a situation in which I have a statistically significant total effect (p<0.05) but both a marginally significant direct and indirect effect (p<0.10). Hence, at the conventional level of significance, neither the direct nor indirect effects are statistically significant. How would you suggest interpreting this situation?

What happens when the other way around is the case, that is, we have two significant coefficients (one is .015 and the other .001; both positive) in a simple path model A->B->C, but the indirect (total) effect is only marginally significant (.06).

Sample size is small (n=129) but then the that should play in the coefficients as well - and it doesn't.

I don't think it is surprising that indirect effects are insignificant when the 2 component effects are significant. Substantively you can think of the A effect as not reaching as far as to C. Statistically, the SE for the product can be larger than for the parts. Also, if this is seen in your construct model version but not in the item-specific versions, then model misspecification may play in as well. The model chi-square may not indicate good fit.

I am running a path model with two mediators, and have used model indirect to get estimates of the specific and total indirect effects. I am puzzled because I have one specific indirect path that is significant (and one not significant), but the total indirect effect is not significant. Is it legitimate to interpret a specific indirect path that is significant, if the total indirect effect is not significant?

Is there a way to test (i.e. get SE's for) a combination of parameters? I am interested in testing the effect of z on y through m (direct + indirect) plus the effect of z*t on y (g1*lam1 + k1 + k2). Relevant part of model is: y2 on z2*0.0244 (k1); y2 on zt2*0 (k2); y2 on m2*0.16 (lam1); m2 on z2*0.16 (g1); [If this matters, I am doing this within a LGC and also MONTECARLO type of data].

Thank you. I created a new parameter (g1*lam1 + k1 + k2) and the value is estimated along with SEs, but for the MONTECARLO data, the true value for the combined effect (against which coverage prob and power are calculated) is not correct in the output. The true value of the combined effect is 0.16*0.16+0.0244+0=0.05, but in the output is listed as 0.5. Is there a way to set the true value for the combined effect other than what I've done above?

I have an interpretation question for a simple mediated model with a single mediator. When I request: y IND m, it shows the 'total' effect from x to y is nonsignficant, but the specific effects show a significant positive indirect effect and a nonsignificant negative direct effect.

My question is, can I still conclude that x is relevant to y (even though the 'total' effect is nonsignificant), in that there was an indirect effect through m?

Hi, I have a model in which I want to test both the total and specific indirect effect from X-->Y through 3 mediators via 4 indirect paths: 1) X-->M1-->Y 2) X-->M2-->Y 3) X-->M1-->M3-->Y 4) X-->M2-->M3-->Y

There are a few questions I would love to have your help: 1) Do I need to include "standardized"in the output row?

2) When reporting the confidence intervals of total/ specific indirect effect, is the normal confidence intervals data or STDYX standardization data to be reported?

3) If STDYX standardization data is to be reported, then I have a significant total indirect effect. In addition, I have 2 indirect path (Path 1 & Path 3) significant at 95% CI and 2 two paths (Path 2 & 4) marginally insignificant at 95% CI (but significant at 90% CI).

Regarding the two marginally insignificant indirect path, what is interesting is that all the component effect (i.e. X->M2, M2->Y, X->M2, M2->M3, M3->Y) are all significant (<.05). In this case, can I still claim that M2 mediate the effect of X on Y? Or how will you interpret the result?

2) That depends largely on the journal you submit to. Personally, I try to avoid standardization when it is not essential. Also, you don't want to use STDYX if X is categorical (see UG).

Regarding your last paragraph, I would report all that. It is the significance of the indirect effect that is the key so I would report that it doesn't reach significance at the 5% level but at the 10% level.

Dear Bengt, Thank you very much for your reply, but it brings me to a more basic question: Re 2, I like your point of avoiding the STDYX. I also have read some articles (introducing me to doing specific mediation using Mplus) which do not report STDYX, but just the normal confidence interval. Why it confuses me is the different result when normal CI or STDYX CI is used. In my case, both CI and STDYX CI report the consistent pattern of result of 90% CI (both do not cover 0, i.e. significant) and 99% CI (both cover 0, i.e. non-significant) for my two ¡°borderline¡± mediation path. But it differs in the 95% CI. If the normal CI is used, then the range of 95% CI will not cover 0 (i.e. significant mediation effect), but the 95% CI will cover 0 if I report the STDYX result (i.e. non-significant). So which one is correct? If STDYX is not compulsory and essential, do you think it will cause problem if I just report normal CI and claim the mediation effect is significant? Or is it better to report the sig. level at all level of CI for the reader's reference? (The journal that I plan to submit is psychology journal rather than statistic journal) Many thanks

There could be small differences between the results for standardized and unstandardized effects. This is due to them having different sampling distributions, with one possibly being more normal than the other. I would report as much as possible of what you have found to give the reader an appreciation for the results.

which is on our website under Papers, Bayesian Analysis. See especially the first path analysis examples for the ATLAS and Firefighter data. With Bayes you can see the whole parameter estimate distribution (the "posterior"), for both unstandardized and standardized estimates, and you can judge which approximates the assumed normal distribution the best. This is a good alternative to bootstrapping when estimate distribution are possibly not normal.

When I want to estimate the indirect path from depr2 to DeltaSK, the total effect is confounded with (for example) depr2 --> af2 --> deltaAF --> DeltaSK. This effect has the opposite direction than depr2 --> af2 --> DeltaSK, because af2 --> DeltaAF is negativ (cealing and floor effects). So the total indirect effects does not make sense. Is it possible to exclude such indirect effects? Or do I have to calculate the total indirect effects? And if so, how can I calculate the SE for a sum of specific indirect effects?

If you want to sum certain indirect effects that are not automatically summed using MODEL INDIRECT, you can use MODEL CONSTRAINT to specify these indirect effects and then create a sum using the NEW option. You will obtain a standard error in that way.

Thanks, it works perfect for the unstand. effect. But how can I get the stdyx-solution? I used additional constraints for the variance of the indep. variable and the dependent variable. But the contraint for the dep. var refers to the residual variance, so this does not work.

I would like to enquire about the indirect effects for a nominal dependent variable. I know, that MPlus v6 does not calculate it, but I am hoping you can advise me on literature regarding this problem. (The article I know from Sobel (1987) only deals with linear structural equations, unfortunately.)

Thank you for your answer. Based on the recommendation of the paper, I tried to run a model. I think I prompted Mplus to calculate the indirect effects, but in the output I got some disturbing results. In the STDYX and STDX Output, my mediating variable seems to be fixed at -1: JP#1 ON EGAL -1.000 0.000 ********* 0.000

This suggests for me that I do not have a correct syntax. I ran the following model:

I would be very greatful, if you would advise me on what I need to fix. Also how I can calculate the standardized coefficients for the two indirect effects? (The example in UG 5.20 has me a bit confused)

I am trying to run a multiple mediation model (with model indirect) with bootstrapping. I am looking at three mediators (m1, m1, m3) and whether they mediate the relation between x (pre-treatment level of problems) to y (post-treatment level of problems).

I have a few questions about this: 1. Under the title of CONFIDENCE INTERVALS FOR TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT AND DIRECT EFFECTS ¡V I seem to only get the Sum of Indirect and Specific Indirect effects -„³ How can I get the estimates and CIs for the Total and the Direct effects as well?

2. I get a significant CI for the Sum of Indirect, which I am interpreting as the Total Indirect suggesting that taken together the three tested mediators have an indirect impact on change from X to Y. Is this correct?

3. How can I get the variance accounted for the Sum of Indirect and/or each Specific Indirect? (I assume the R quared in the output pertains to the direct paths to Y?)

3. Two of the specific Indirect effects are also significant - is it okay to interpret these as significant mediators?

Further to my question above, I am wondering whether I also need to say something about the direct effects of X on Y? a) where to I find information about whether X on Y is significant in this model? b) if X on Y is significant in the meditational model, yet there are also the indirect effects described above does this suggest partial mediation? Or?

Thank you for your answer. I have reviewed the suggested paper several times, as well as corresponding papers and it is not clear to me: should I be building up my analysis for the continuous meditator with nominal outcome

from the example, where there is a continous mediator and a binary outcome

OR

from the example, where a nominal variable is the mediator variable on a continuous outcome?

(I have mainly experimented with the first version). Thank you again for your help, Zsofia Ignacz

thank you so much for your response and my appologies for the multiple messages!

I just have a follow-up question - would you recommend calculating the total effect (sum of the indirect and direct effect) given that without a CI it is not possible to interpret? Or is reporting the total indirect and specific indirect effects suffcient?

Thank you very much for your answer! I already considered this, I was just hoping that I could condense my model and I overlooked something...Then I will try to calculate the estimates by hand, taking into consideration the bias of the logistic function.

If the direct effect of A on D was non-significant, the total effect of A on D is: (a)*(b)*(c) [the product of the three path coeffieints]

Is this product still standardized beta? If not, what should this product (indirect effect) be labelled as?

I am having difficulty interpreting my result since multiplicative product of the three paths was .01 and I'm not sure if that should be interpreted as a path coefficient (or is it the amount of variance explained as R square is in regression contexxt?).

I would not use the standardized coefficients. I would multiply the raw coefficients and standardize by a and d. So multiply by the standard deviation of a and divide by the standard deviation of d. This is a regression coefficient not an R-square.

we estimated a path model with one dummy-coded predictor variable (X), one continuous mediator (M), and two continuous criterion variables (Y, Z). We used a bias-based bootstrapping procedure (in MPlus Version 5.2) and found indirect, but no direct or total effects from X on Y and from X on Z. We would like to know why we have significant indirect, but no total effects. We know that total effects can be suppressed when indirect and direct effects are opposite in sign. This is, however, not the case in our analysis (the total effects are greater than the corresponding indirect effects). We noticed that the standard errors of the direct and total effects (from X on Y/Z) are much greater than the standard errors of the indirect effects and would be pleased if you could help us understand why this is so. 1.Why are the standard errors of the direct effects higher than the standard errors of the indirect effects? 2.How is the standard error of the total effect (X-->Y) estimated in MPlus? In what way does the standard error of the direct effect (X-->Y) influence the estimation of the standard error of the total effect? 3. By comparison: How is the standard error of the indirect effect estimated in MPlus? 4. Do you have any other ideas on how to explain why we have significant indirect, but no total effects?

Hope you are well! My coauthors and I have been puzzling over a similar situation to that above, where the indirect effect is significant but the total effect (which is larger) is non-significant due to a much larger SE. I wondered if there was an explanation for this or if, based on your request for the output above, this might indicate an issue with our models?

I am happy to send the output and license number if relevant, but wanted to see if this was actually an issue or if there might be some explanation first!